An overview of results is given for laser ion sources based on the expanding laser plasma. All these experiments serve as a base for studies of possible, but not yet unambiguously determined mechanisms of ion production under various experimental conditions. The thermal ambipolar acceleration of ions guided either by thermal or suprathermal electrons, are assumed to be responsible for the ion streams expanding backward from the massive targets and registered by standard corpuscular diagnostics methods. A multi peak structure of the ion energy spectra is the most conspicuous phenomenon suggesting the presence of several fast electron groups guiding the plasma expansion and assisting the charge freezing due to the enhanced acceleration. The frequently observed asymmetry of the ion with respect to the laser caustic can be interpreted as the onset of self focusing of the heating laser beam inside the self-created plasma of the developing laser corona (or a pre-pulse plasma either formed by a double pulse or generated spontaneously in the case of a low contrast of the heating pulse) with a dramatic increase in the power density impinging on the target.